A Los Angeles County man was arrested Wednesday after what authorities characterized as the apparent mercy killings of his wife at their home and his sister in a nursing home where she had been comatose for five years.

The family of Lance Holger Anderson said his 63-year-old wife was suffering from dementia, said police Lt. Paul Vernon. She was killed in their apartment in the Canyon Country section of Santa Clarita, about 35 miles northwest of downtown Los Angeles.

Police said the 60-year-old Anderson then drove to Country Villa Sheraton Nursing Rehabilitation Hospital in North Hills, where he allegedly shot his sister once in the head with a small-caliber handgun around 9:20 a.m. (12:20 p.m. ET). He went outside and waited for police.

The sister was identified by police as Lisa Nave, 58, who had been in a coma since suffering a heart attack.

Authorities said the suspect had applied for a job at the nursing facility, KCAL-TV reported.

"I use the term 'mercy killing' in terms of describing a killing here because I want people to understand that this man did not randomly walk into a hospital to commit this crime," Vernon told the Los Angeles Times. He said two other unconscious patients nearby were not harmed.

After the shooting, Nave's family became concerned about the suspect's wife and asked the sheriff's department to check on her. Deputies found her shot to death, apparently with the same gun used to kill Nave.

Two weeks ago, the Times writes, Anderson gave away his Christmas tree to neighbor, telling her, "We're not having Christmas this year."